Unit 2: Newton's Laws
Big Ideas:
1. Newton's Laws of Motion are used to analyze how force affects the state of motion of an object.
2. Motion is always measured relative to an arbitrary frame of reference.
3. All uniform circular motion requires a centripetal force.
Learner Objectives (as published by the College Board):
1. Students should be able to analyze situations in which a particle remains at rest, or moves with constant velocity, under the influence of several forces.
2. Students should understand the relation between the force
that acts on an object and the resulting change in the object's velocity, so
they can:
A. Calculate, for an object moving in one dimension, the
velocity change that results when a constant force F acts over a specified time
interval.
B. Calculate, for an object moving in one dimension, the
velocity change that results when a force F(t) acts over a specified time
interval.
C. Determine, for an object moving in a plane whose velocity
vector undergoes a specified change over a specified time interval, the average
force that acted on the object.
3. Students should understand how Newton's Second Law, ∑F = ma, applies
to an object subject to forces such as gravity, the pull of strings, or contact
forces, so they can:
A. Draw a well-labeled, free-body diagram showing all real
forces that act on the object.
B. Write down the vector equation that results from applying
Newton's Second Law to the object, and take components of this equation along
appropriate axes.
4. Students should be able to analyze situations in which an
object moves with specified acceleration under the influence of one or more
forces so they can determine the magnitude and direction of the net force, or
of one of the forces that makes up the net force, such as motion up or down
with constant acceleration.
5. Students should understand the significance of the
coefficient of friction, so they can:
A. Write down the relationship between the normal and
frictional forces on a surface.
B. Analyze situations in which an object moves along a rough
inclined plane or horizontal surface.
C. Analyze under what circumstances an object will start to
slip, or to calculate the magnitude of the force of static friction.
6. Students should understand the effect of drag forces on
the motion of an object, so they can:
A. Find the terminal velocity of an object moving vertically
under the influence of a retarding force dependent on velocity.
B. Describe qualitatively, with the aid of graphs, the
acceleration, velocity, and displacement of such a particle when it is released
from rest or is projected vertically with specified initial velocity.
C. Use Newton's Second Law to write a differential equation
for the velocity of the object as a function of time.
D. Use the method of separation of variables to derive the
equation for the velocity as a function of time from the differential equation
that follows from Newton's Second Law.
E. Derive an expression for the acceleration as a function
of time for an object falling under the influence of drag forces.
7. Students should understand Newton's Third Law so that,
for a given system, they can identify the force pairs and the objects on which
they act, and state the magnitude and direction of each force.
8. Students should be able to apply Newton's Third Law in
analyzing the force of contact between two objects that accelerate together
along a horizontal or vertical line, or between two surfaces that slide across
one another.
9. Students should know that the tension is constant in a
light string that passes over a massless pulley and should be able to use this
fact in analyzing the motion of a system of two objects joined by a string.
10. Students should be able to solve problems in which application of Newton's laws leads to two or three simultaneous linear
equations involving unknown forces or accelerations.
11. Students should understand the uniform circular motion of a particle, so they can analyze situations in which an object moves with specified acceleration under the influence of one or more forces and determine the magnitude and direction of the net force, or of one of the forces that makes up the net force, in situations such as the following:
A. Motion in a horizontal circle (e.g., mass on a rotating merry-go-round, or car rounding a banked curve).
B. Motion in a vertical circle (e.g., mass swinging on the end of a string, cart rolling down a curved track, rider on a Ferris wheel).